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Open AccessArticle

Some Properties of the Fuss–Catalan Numbers

by Feng Qi 1,2,3,* and Pietro Cerone 4
1
Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, Henan, China
2
College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, Inner Mongolia, China
3
School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China
4
Department of Mathematics and Statistics, La Trobe University, Melbourne (Bundoora) 3086, Victoria, Australia
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(12), 277; https://doi.org/10.3390/math6120277
Received: 31 October 2018 / Revised: 12 November 2018 / Accepted: 14 November 2018 / Published: 24 November 2018
(This article belongs to the Special Issue Special Functions and Applications)
In the paper, the authors express the Fuss–Catalan numbers as several forms in terms of the Catalan–Qi function, find some analytic properties, including the monotonicity, logarithmic convexity, complete monotonicity, and minimality, of the Fuss–Catalan numbers, and derive a double inequality for bounding the Fuss–Catalan numbers. View Full-Text
Keywords: Fuss–Catalan number; Catalan–Qi function; Catalan number; monotonicity; logarithmic convexity; complete monotonicity; minimality; inequality Fuss–Catalan number; Catalan–Qi function; Catalan number; monotonicity; logarithmic convexity; complete monotonicity; minimality; inequality
MDPI and ACS Style

Qi, F.; Cerone, P. Some Properties of the Fuss–Catalan Numbers. Mathematics 2018, 6, 277.

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